(************** Content-type: application/mathematica **************
                     CreatedBy='Mathematica 5.1'

                    Mathematica-Compatible Notebook

This notebook can be used with any Mathematica-compatible
application, such as Mathematica, MathReader or Publicon. The data
for the notebook starts with the line containing stars above.

To get the notebook into a Mathematica-compatible application, do
one of the following:

* Save the data starting with the line of stars above into a file
  with a name ending in .nb, then open the file inside the
  application;

* Copy the data starting with the line of stars above to the
  clipboard, then use the Paste menu command inside the application.

Data for notebooks contains only printable 7-bit ASCII and can be
sent directly in email or through ftp in text mode.  Newlines can be
CR, LF or CRLF (Unix, Macintosh or MS-DOS style).

NOTE: If you modify the data for this notebook not in a Mathematica-
compatible application, you must delete the line below containing
the word CacheID, otherwise Mathematica-compatible applications may
try to use invalid cache data.

For more information on notebooks and Mathematica-compatible 
applications, contact Wolfram Research:
  web: http://www.wolfram.com
  email: info@wolfram.com
  phone: +1-217-398-0700 (U.S.)

Notebook reader applications are available free of charge from 
Wolfram Research.
*******************************************************************)

(*CacheID: 232*)


(*NotebookFileLineBreakTest
NotebookFileLineBreakTest*)
(*NotebookOptionsPosition[     14361,        562]*)
(*NotebookOutlinePosition[     15068,        586]*)
(*  CellTagsIndexPosition[     15024,        582]*)
(*WindowFrame->Normal*)



Notebook[{

Cell[CellGroupData[{
Cell[TextData[{
  StyleBox["Calculations ", "Section"],
  "\n\nfor \nWage Dispersion, Over-Qualification, and Reder Competition\nby \
Ekkehart Schlicht\n\neconomics - The Open-Access, Open-Assessment E-Journal, \
2007-13. http://www.economics-ejournal.org/economics/journalarticles/2007-13 \
"
}], "Subsubtitle"],

Cell[CellGroupData[{

Cell["Paper", "Subsection"],

Cell[CellGroupData[{

Cell["Clear all symbols", "Subsubsection"],

Cell[BoxData[
    \(\(Quit[];\)\)], "Input"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Definitions (1) - (3)", "Subsubsection"],

Cell[BoxData[{
    \(\(profit = \ p\ \[Alpha]\  - w - c;\)\), "\[IndentingNewLine]", 
    \(\(\[Rho] = q \((1 + \[Mu]\ Log[w\/W])\);\)\), "\[IndentingNewLine]", 
    \(\(\[Alpha] = \[Rho]\ x + \((1 - \[Rho])\) 
            y;\)\), "\[IndentingNewLine]", 
    \(\)}], "Input"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Zero profit price (6)", "Subsubsection"],

Cell[CellGroupData[{

Cell[BoxData[{
    \(\(W = w;\)\), "\[IndentingNewLine]", 
    \(Solve[{profit \[Equal] 0}, p]\), "\[IndentingNewLine]", 
    \(\)}], "Input"],

Cell[BoxData[
    \({{p \[Rule] \(c + w\)\/\(q\ x + y - q\ y\)}}\)], "Output"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Clear the assignment W=w", "Subsubsection"],

Cell[BoxData[
    \(Clear[W]\)], "Input"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Check  equation (6)", "Subsubsection"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[\(c + W\)\/\(q\ x + y - q\ y\) == \(W + c\)\/\(q\ \((x - y)\) \
+ y\)]\)], "Input"],

Cell[BoxData[
    \(True\)], "Output"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Selection wage curve (7) - (9)", "Subsubsection"],

Cell[BoxData[{
    \(\(Dprofit = D[profit, w];\)\), "\[IndentingNewLine]", 
    \(\(D2profit = D[profit, {w, 2}];\)\), "\[IndentingNewLine]", 
    \(\(W = w;\)\), "\[IndentingNewLine]", 
    \(\)}], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[
      Dprofit \[Equal] \ p\ q\ \[Mu] \((x - y)\) 1\/w - 1]\)], "Input"],

Cell[BoxData[
    \(True\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[
      D2profit \[Equal] \ \(-p\)\ q\ \[Mu] \((x - y)\) 1\/w\^2]\)], "Input"],

Cell[BoxData[
    \(True\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Solve[Dprofit \[Equal] 0, p]\)], "Input"],

Cell[BoxData[
    \({{p \[Rule] w\/\(q\ \((x - y)\)\ \[Mu]\)}}\)], "Output"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Equilibrium (10), (11)", "Subsubsection"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Solve[{profit \[Equal] 0, Dprofit \[Equal] 0}, {w, p}]\)], "Input"],

Cell[BoxData[
    \({{w \[Rule] \(-\(\(c\ \((q\ x\ \[Mu] - q\ y\ \[Mu])\)\)\/\(\(-q\)\ x - 
                  y + q\ y + q\ x\ \[Mu] - q\ y\ \[Mu]\)\)\), 
        p \[Rule] \(-\(c\/\(\(-q\)\ x - y + q\ y + q\ x\ \[Mu] - 
                  q\ y\ \[Mu]\)\)\)}}\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[\(-\(\(c\ \((q\ x\ \[Mu] - q\ y\ \[Mu])\)\)\/\(\(-q\)\ x - y + 
                q\ y + q\ x\ \[Mu] - 
                q\ y\ \[Mu]\)\)\) == \(\(\(\[Mu]\)\(\ \)\(q\)\(\ \)\((x - 
                    y)\)\(\ \)\)\/\(q \((x - y)\) \((1 - \[Mu])\) + y\)\) 
          c]\)], "Input"],

Cell[BoxData[
    \(True\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[\(-\(c\/\(\(-q\)\ x - y + q\ y + q\ x\ \[Mu] - 
                q\ y\ \[Mu]\)\)\) == 
        c\/\(q \((x - y)\) \((1 - \[Mu])\) + y\)]\)], "Input"],

Cell[BoxData[
    \(True\)], "Output"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Stability (12)", "Subsubsection"],

Cell[BoxData[
    \(\(Clear[W];\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Solve[p\ q\ \[Mu] \((x - y)\) 1\/w - 1 \[Equal] 0, w]\)], "Input"],

Cell[BoxData[
    \({{w \[Rule] p\ q\ x\ \[Mu] - p\ q\ y\ \[Mu]}}\)], "Output"]
}, Open  ]],

Cell[BoxData[
    \(\(p = \(W + c\)\/\(q \((x - y)\) + y\);\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(w = p\ q\ x\ \[Mu] - p\ q\ y\ \[Mu]\)], "Input"],

Cell[BoxData[
    \(\(q\ \((c + W)\)\ x\ \[Mu]\)\/\(q\ \((x - y)\) + y\) - \(q\ \((c + W)\)\
\ y\ \[Mu]\)\/\(q\ \((x - y)\) + y\)\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[\((\(q\ \((c + W)\)\ x\ \[Mu]\)\/\(q\ \((x - y)\) + y\) - \(q\ \
\((c + W)\)\ y\ \[Mu]\)\/\(q\ \((x - y)\) + y\))\) == \(\(\[Mu] \((x - y)\) 
                q\)\/\(\((x - y)\) q + y\)\) \((W + c)\)]\)], "Input"],

Cell[BoxData[
    \(True\)], "Output"]
}, Open  ]],

Cell[BoxData[
    \(\(\(W\&_ = \(\(\(\[Mu]\)\(\ \)\(q\)\(\ \)\((x - 
                    y)\)\(\ \)\)\/\(q \((x - y)\) \((1 - \[Mu])\) + y\)\) 
          c;\)\(\[IndentingNewLine]\)
    \)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[\((w - 
            W)\) \[Equal] \(-\(\(\((1 - \[Mu])\) \((x - y)\) q + 
                  y\)\/\(\((x - y)\) q + y\)\)\) \((W - W\&_)\)]\)], "Input"],

Cell[BoxData[
    \(True\)], "Output"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Inequality (13)", "Subsubsection"],

Cell[BoxData[
    \(\(Clear[W, p];\)\)], "Input"],

Cell["\<\
Condition is given wrongly in the manuscript. It should relate to mediocre \
productivity y rather than prolific productivity x and read\
\>", "Text"],

Cell[BoxData[
    \(p\ y > W\)], "Input"],

Cell["and inequalities (13) should read", "Text"],

Cell[BoxData[
    \(y > \(q\ x\ \[Mu]\)\/\(1 + q\ \[Mu]\)\ and\ \[Mu]\ q\  < \ 
      y\/\(x - y\)\)], "Input"],

Cell["\<\
Replacing the inequality with equality, I check whether these inequalities \
are  equivalent to p y > W.\
\>", "Text"],

Cell[BoxData[
    \(\(p\&_ = c\/\(y + q\ \((x - y)\)\ \((1 - \[Mu])\)\);\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Solve[p\&_\ y == W\&_\ \ , y]\)], "Input"],

Cell[BoxData[
    \({{y \[Rule] \(q\ x\ \[Mu]\)\/\(1 + q\ \[Mu]\)}}\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Solve[p\&_\ y == W\&_\ \ , q]\)], "Input"],

Cell[BoxData[
    \({{q \[Rule] \(-\(y\/\(\((\(-x\) + y)\)\ \[Mu]\)\)\)}}\)], "Output"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Quality mix (14) and (15)", "Subsubsection"],

Cell[CellGroupData[{

Cell[BoxData[
    \(D[W\&_, q]\)], "Input"],

Cell[BoxData[
    \(\(c\ \((x - y)\)\ \[Mu]\)\/\(y + q\ \((x - y)\)\ \((1 - \[Mu])\)\) - \
\(c\ q\ \((x - y)\)\^2\ \((1 - \[Mu])\)\ \[Mu]\)\/\((y + q\ \((x - y)\)\ \((1 \
- \[Mu])\))\)\^2\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[\((\(c\ \((x - y)\)\ \[Mu]\)\/\(y + q\ \((x - y)\)\ \((1 - \
\[Mu])\)\) - \(c\ q\ \((x - y)\)\^2\ \((1 - \[Mu])\)\ \[Mu]\)\/\((y + q\ \((x \
- y)\)\ \((1 - \[Mu])\))\)\^2)\) \[Equal] \(\((1\/\(q \((x - y)\)\ \((1 - \
\[Mu])\) + y\))\)\^2\) c\ \((x - y)\) y\ \[Mu]]\)], "Input"],

Cell[BoxData[
    \(True\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(D[p\&_, q]\)], "Input"],

Cell[BoxData[
    \(\(-\(\(c\ \((x - 
                y)\)\ \((1 - \[Mu])\)\)\/\((y + q\ \((x - y)\)\ \((1 - \[Mu])\
\))\)\^2\)\)\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[\(-\(\(c\ \((x - 
                    y)\)\ \((1 - \[Mu])\)\)\/\((y + q\ \((x - y)\)\ \((1 - \
\[Mu])\))\)\^2\)\) \[Equal] \(-\((1\/\(q \((x - y)\)\ \((1 - \[Mu])\) + \
y\))\)\^2\) c \((x - y)\) \((1 - \[Mu])\)]\)], "Input"],

Cell[BoxData[
    \(True\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[\(c\ q\ \((x - y)\)\ \((q\ \((x - y)\) + y)\)\ \[Mu]\)\/\(\((c \
+ W)\)\ \((y + q\ \((x - y)\)\ \((1 - \[Mu])\))\)\)]\)], "Input"],

Cell[BoxData[
    \(\(c\ q\ \((x - y)\)\ \((q\ \((x - y)\) + y)\)\ \[Mu]\)\/\(\((c + W)\)\ \
\((y - q\ \((x - y)\)\ \((\(-1\) + \[Mu])\))\)\)\)], "Output"]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Appendix: Performance Pay", "Subsection"],

Cell[BoxData[
    \(\(Clear[p, W, w];\)\)], "Input"],

Cell[CellGroupData[{

Cell["The profit function  (17) is", "Subsubsection"],

Cell[BoxData[{
    RowBox[{
      RowBox[{"prof", "=", 
        RowBox[{
          RowBox[{"p", 
            RowBox[{"(", 
              RowBox[{\(\[Rho]\ x\), " ", "+", 
                RowBox[{
                  RowBox[{"(", 
                    RowBox[{"1", "-", 
                      FormBox["\[Rho]",
                        "InputForm"]}], ")"}], "y"}]}], ")"}]}], "-", 
          RowBox[{
            FormBox["\[Rho]",
              "InputForm"], " ", "w"}], " ", "-", 
          RowBox[{
            RowBox[{"(", 
              RowBox[{"1", "-", 
                FormBox["\[Rho]",
                  "InputForm"]}], ")"}], " ", \(y\/x\), " ", "w"}], " ", "-", 
          "c"}]}], 
      ";"}], "\[IndentingNewLine]", \(\[Rho] = 
        q \((1 + \[Mu]\ Log[w\/W])\);\)}], "Input"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Its derivative with respect to w is", "Subsubsection"],

Cell[BoxData[{
    \(\(Dprof = D[prof, w];\)\), "\[IndentingNewLine]", 
    \(\(W = w;\)\)}], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(solution = 
      Solve[{Dprof \[Equal] 0, prof \[Equal] 0}, {w, p}]\)], "Input"],

Cell[BoxData[
    \({{w \[Rule] \(-\(\(\(-c\)\ q\ x\^2\ \[Mu] + 
                  c\ q\ x\ y\ \[Mu]\)\/\((q\ x + y - q\ y)\)\^2\)\), 
        p \[Rule] \(-\(\(\(-c\)\ q\ x - c\ y + c\ q\ y - c\ q\ x\ \[Mu] + 
                  c\ q\ y\ \[Mu]\)\/\((q\ x + y - q\ y)\)\^2\)\)}}\)], \
"Output"]
}, Open  ]],

Cell[BoxData[""], "Input"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Check that  expression (18) is correct", "Subsubsection"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[\(-\(\(\(-c\)\ q\ x\^2\ \[Mu] + 
                c\ q\ x\ y\ \[Mu]\)\/\((q\ x + y - q\ y)\)\^2\)\) \[Equal] \ 
        c\ q\ x\ \[Mu] \(\(\ \)\(\(x\)\(-\)\(y\)\(\ \)\)\)\/\((q\ x + \((1 - \
q)\) y)\)\^2]\)], "Input"],

Cell[BoxData[
    \(True\)], "Output"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Compare flat pay with performance pay", "Subsubsection"],

Cell[BoxData[
    \(Clear[W]\)], "Input"],

Cell[BoxData[{
    \(\(W\&~ = 
        c\ q\ x\ \[Mu] \(\(\ \)\(\(x\)\(-\)\(y\)\(\ \)\)\)\/\((q\ x + \((1 - \
q)\) y)\)\^2;\)\), "\[IndentingNewLine]", 
    \(\(V\&~ = \(y\/x\) W\&~;\)\), "\[IndentingNewLine]", 
    \(\(W\&_\  = \(\(\(\[Mu]\)\(\ \)\(q\)\(\ \)\((x - 
                    y)\)\(\ \)\)\/\(q \((x - y)\) \((1 - \[Mu])\) + y\)\) 
          c;\)\), "\[IndentingNewLine]", 
    \(\)}], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[\((W\&_ - \((q\ W\&~ + \((1 - q)\) 
                  V\&~)\))\) == \(c\ q\^2\ \((x - y)\)\^2\ \[Mu]\^2\)\/\(\((q\
\ x + \((1 - q)\) y)\)\ \((q\ \((x - y)\)\ \((1 - \[Mu])\) + y)\)\)]\)], \
"Input"],

Cell[BoxData[
    \(True\)], "Output"]
}, Open  ]],

Cell[BoxData[""], "Input"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Wage Compression", "Subsection"],

Cell[BoxData[
    \(\(Clear[p, W, V];\)\)], "Input"],

Cell[CellGroupData[{

Cell["The Lagrangean is", "Subsubsection"],

Cell[BoxData[
    \(\(\(\[IndentingNewLine]\)\(L = 
        q \((1 + \ \[Mu]\ Log[w\/W])\) \((p\ x - w)\) + \((1 - 
                q)\) \((1 + \ \[Mu]\ Log[v\/V])\) \((p\ y - v)\) - 
          c - \[Lambda] \((q\ Log[w\/W] + \((1 - q)\)\ Log[
                    v\/V])\);\)\)\)], "Input"]
}, Open  ]],

Cell[CellGroupData[{

Cell["The derivatives at w=W are", "Subsubsection"],

Cell[BoxData[{
    \(\(DLw = D[L, w];\)\), "\[IndentingNewLine]", 
    \(\(DLv\  = D[L, v];\)\), "\[IndentingNewLine]", 
    \(\)}], "Input"],

Cell[CellGroupData[{

Cell[BoxData[{
    \(\(W = w;\)\), "\[IndentingNewLine]", 
    \(Simplify[
      DLw == \(q\/w\) \((\((p\ x - w)\) \[Mu] - \[Lambda] - w)\)]\)}], "Input"],

Cell[BoxData[
    \(True\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
    \(\(V = v;\)\), "\[IndentingNewLine]", 
    \(Simplify[
      DLv == \(\(1 - q\)\/v\) \((\((p\ y - v)\) \[Mu] - \[Lambda] - 
              v)\)]\)}], "Input"],

Cell[BoxData[
    \(True\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(\(\(Solve[{DLw \[Equal] 0, DLv \[Equal] 0}, {v, 
        w}]\)\(\[IndentingNewLine]\)
    \)\)], "Input"],

Cell[BoxData[
    \({{w \[Rule] \(\(-\[Lambda]\) + p\ x\ \[Mu]\)\/\(1 + \[Mu]\), 
        v \[Rule] \(\(-\[Lambda]\) + p\ y\ \[Mu]\)\/\(1 + \[Mu]\)}}\)], \
"Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[\(\(-\[Lambda]\) + p\ x\ \[Mu]\)\/\(1 + \[Mu]\) - \(\(-\
\[Lambda]\) + p\ y\ \[Mu]\)\/\(1 + \[Mu]\)]\)], "Input"],

Cell[BoxData[
    \(\(p\ \((x - y)\)\ \[Mu]\)\/\(1 + \[Mu]\)\)], "Output"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}, Open  ]]
},
FrontEndVersion->"5.1 for Microsoft Windows",
ScreenRectangle->{{0, 1280}, {0, 947}},
WindowSize->{918, 714},
WindowMargins->{{60, Automatic}, {Automatic, 18}},
PrintingCopies->1,
PrintingPageRange->{Automatic, Automatic}
]

(*******************************************************************
Cached data follows.  If you edit this Notebook file directly, not
using Mathematica, you must remove the line containing CacheID at
the top of  the file.  The cache data will then be recreated when
you save this file from within Mathematica.
*******************************************************************)

(*CellTagsOutline
CellTagsIndex->{}
*)

(*CellTagsIndex
CellTagsIndex->{}
*)

(*NotebookFileOutline
Notebook[{

Cell[CellGroupData[{
Cell[1776, 53, 312, 6, 176, "Subsubtitle"],

Cell[CellGroupData[{
Cell[2113, 63, 27, 0, 38, "Subsection"],

Cell[CellGroupData[{
Cell[2165, 67, 42, 0, 29, "Subsubsection"],
Cell[2210, 69, 44, 1, 30, "Input"]
}, Open  ]],

Cell[CellGroupData[{
Cell[2291, 75, 46, 0, 29, "Subsubsection"],
Cell[2340, 77, 275, 5, 102, "Input"]
}, Open  ]],

Cell[CellGroupData[{
Cell[2652, 87, 46, 0, 29, "Subsubsection"],

Cell[CellGroupData[{
Cell[2723, 91, 142, 3, 70, "Input"],
Cell[2868, 96, 78, 1, 42, "Output"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{
Cell[2995, 103, 49, 0, 29, "Subsubsection"],
Cell[3047, 105, 41, 1, 30, "Input"]
}, Open  ]],

Cell[CellGroupData[{
Cell[3125, 111, 44, 0, 29, "Subsubsection"],

Cell[CellGroupData[{
Cell[3194, 115, 112, 2, 44, "Input"],
Cell[3309, 119, 38, 1, 29, "Output"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{
Cell[3396, 126, 55, 0, 29, "Subsubsection"],
Cell[3454, 128, 207, 4, 90, "Input"],

Cell[CellGroupData[{
Cell[3686, 136, 101, 2, 42, "Input"],
Cell[3790, 140, 38, 1, 29, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[3865, 146, 106, 2, 42, "Input"],
Cell[3974, 150, 38, 1, 29, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[4049, 156, 61, 1, 30, "Input"],
Cell[4113, 159, 76, 1, 42, "Output"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{
Cell[4238, 166, 47, 0, 29, "Subsubsection"],

Cell[CellGroupData[{
Cell[4310, 170, 87, 1, 30, "Input"],
Cell[4400, 173, 272, 4, 44, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[4709, 182, 306, 5, 44, "Input"],
Cell[5018, 189, 38, 1, 29, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[5093, 195, 177, 3, 42, "Input"],
Cell[5273, 200, 38, 1, 29, "Output"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{
Cell[5360, 207, 39, 0, 29, "Subsubsection"],
Cell[5402, 209, 46, 1, 30, "Input"],

Cell[CellGroupData[{
Cell[5473, 214, 86, 1, 42, "Input"],
Cell[5562, 217, 79, 1, 29, "Output"]
}, Open  ]],
Cell[5656, 221, 74, 1, 44, "Input"],

Cell[CellGroupData[{
Cell[5755, 226, 68, 1, 30, "Input"],
Cell[5826, 229, 143, 2, 44, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[6006, 236, 241, 3, 44, "Input"],
Cell[6250, 241, 38, 1, 29, "Output"]
}, Open  ]],
Cell[6303, 245, 201, 4, 65, "Input"],

Cell[CellGroupData[{
Cell[6529, 253, 180, 3, 44, "Input"],
Cell[6712, 258, 38, 1, 29, "Output"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{
Cell[6799, 265, 40, 0, 29, "Subsubsection"],
Cell[6842, 267, 49, 1, 30, "Input"],
Cell[6894, 270, 160, 3, 33, "Text"],
Cell[7057, 275, 41, 1, 30, "Input"],
Cell[7101, 278, 49, 0, 33, "Text"],
Cell[7153, 280, 111, 2, 42, "Input"],
Cell[7267, 284, 128, 3, 33, "Text"],
Cell[7398, 289, 87, 1, 42, "Input"],

Cell[CellGroupData[{
Cell[7510, 294, 62, 1, 31, "Input"],
Cell[7575, 297, 81, 1, 42, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[7693, 303, 62, 1, 31, "Input"],
Cell[7758, 306, 87, 1, 42, "Output"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{
Cell[7894, 313, 50, 0, 29, "Subsubsection"],

Cell[CellGroupData[{
Cell[7969, 317, 43, 1, 31, "Input"],
Cell[8015, 320, 201, 3, 47, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[8253, 328, 306, 4, 47, "Input"],
Cell[8562, 334, 38, 1, 29, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[8637, 340, 43, 1, 30, "Input"],
Cell[8683, 343, 143, 3, 44, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[8863, 351, 253, 4, 45, "Input"],
Cell[9119, 357, 38, 1, 29, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[9194, 363, 159, 2, 44, "Input"],
Cell[9356, 367, 155, 2, 44, "Output"]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{
Cell[9572, 376, 47, 0, 38, "Subsection"],
Cell[9622, 378, 52, 1, 30, "Input"],

Cell[CellGroupData[{
Cell[9699, 383, 53, 0, 29, "Subsubsection"],
Cell[9755, 385, 788, 22, 71, "Input"]
}, Open  ]],

Cell[CellGroupData[{
Cell[10580, 412, 60, 0, 29, "Subsubsection"],
Cell[10643, 414, 102, 2, 50, "Input"],

Cell[CellGroupData[{
Cell[10770, 420, 101, 2, 30, "Input"],
Cell[10874, 424, 292, 5, 47, "Output"]
}, Open  ]],
Cell[11181, 432, 26, 0, 30, "Input"]
}, Open  ]],

Cell[CellGroupData[{
Cell[11244, 437, 63, 0, 29, "Subsubsection"],

Cell[CellGroupData[{
Cell[11332, 441, 245, 4, 47, "Input"],
Cell[11580, 447, 38, 1, 29, "Output"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{
Cell[11667, 454, 62, 0, 29, "Subsubsection"],
Cell[11732, 456, 41, 1, 30, "Input"],
Cell[11776, 459, 404, 8, 131, "Input"],

Cell[CellGroupData[{
Cell[12205, 471, 227, 4, 47, "Input"],
Cell[12435, 477, 38, 1, 29, "Output"]
}, Open  ]],
Cell[12488, 481, 26, 0, 30, "Input"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{
Cell[12563, 487, 38, 0, 38, "Subsection"],
Cell[12604, 489, 52, 1, 30, "Input"],

Cell[CellGroupData[{
Cell[12681, 494, 42, 0, 29, "Subsubsection"],
Cell[12726, 496, 290, 5, 61, "Input"]
}, Open  ]],

Cell[CellGroupData[{
Cell[13053, 506, 51, 0, 29, "Subsubsection"],
Cell[13107, 508, 141, 3, 70, "Input"],

Cell[CellGroupData[{
Cell[13273, 515, 154, 3, 61, "Input"],
Cell[13430, 520, 38, 1, 29, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[13505, 526, 177, 4, 63, "Input"],
Cell[13685, 532, 38, 1, 29, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[13760, 538, 125, 3, 50, "Input"],
Cell[13888, 543, 165, 3, 44, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[14090, 551, 142, 2, 44, "Input"],
Cell[14235, 555, 74, 1, 44, "Output"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}
]
*)



(*******************************************************************
End of Mathematica Notebook file.
*******************************************************************)

